Postdoctoral position in Mathematical Logic & Mathematical Statistics, Toronto (Canada)
The University of Toronto seeks a Postdoctoral Researcher to conduct collaborative research outlined in an awarded NFRFE-2018 New Frontier in Research proposal, titled 'Rebuilding the Foundations of Bayesian Statistics on Nonstandard Analysis' (PI: Daniel M. Roy).
Our proposal aims to rebuild the mathematical foundations of Bayesian statistics using tools from mathematical logic and nonstandard analysis that were unavailable at the time Bayesian analysis was formalized. Our goal is to tackle one of the grand challenges in mathematical statistics: fully characterize the relationship between Bayesian and frequentist inference, the two dominant approaches to statistical inference. In recent work, replacing the standard model of countably additive probability theory with a nonstandard model allowed us to settle a longstanding open problem of deriving a Bayesian characterization of frequentist extended admissibility. We believe that rapid progress on the grand challenge can be achieved by committing additional resources to this unconventional approach.